Discrete Geometry: From Graphics to Physically-based Simulation
Michigan State University
Tuesday, April 8, 2008
9:45 a.m. – 10:45 a.m.
Host: Eric Torng
In this talk, we present some of our recent work in computer graphics and simulation to demonstrate the value of a structure-preserving discretization of geometry. We first review an Eulerian approach to discrete geometric shapes based on the concept of chain in algebraic topology, with applications in MRI medical dataset smoothing and incompressible fluid simulation. We then present a general framework for calculus on meshes. The framework is built on a formal discretization of Cartan's exterior calculus of differential forms. Applying this general framework to geometric modeling, we show various algorithms for geometric texture synthesis, quadrangulation of triangular meshes, and surface reconstruction from point sets. With the exact same framework, we demonstrate how fluid simulation on simplicial complexes can be implemented in an intrinsic manner through proper discretization of flux and vorticity. Extending the framework to general dynamics, we finally show how the preservation of geometric structures directly leads to numerically-superior time integrators.
Yiying Tong is a Research Associate in the Department of Computer Science and Engineering at Michigan State University. Prior to joining MSU, He worked as a postdoctoral scholar at Caltech. He received his Ph.D. degree from University of Southern California in 2004. His research interests include discrete geometric modeling, physically-based simulation/animation, and discrete differential geometry. He has published 6 SIGGRAPH papers. His list of publications is available at www.cse.msu.edu/~ytong.